La. Admin. Code tit. 28 § CLXXI-2103

Current through Register Vol. 50, No. 8, August 20, 2024

Section CLXXI-2103 - Algebra

A. Interpret expressions that represent a quantity in terms of its context.

1. Interpret parts of an expression, such as terms, factors, and coefficients.

2. Interpret complicated expressions by viewing one or more of their parts as a single entity.

Example: Interpret P(1+r)n as the product of P and a factor not depending on P.

B. Use the structure of an expression to identify ways to rewrite it.

Example: x⁴ - y⁴ as (x²)² -(y²)², thus recognizing it as a difference of squares that can be factored as (x² - y²)(x² + y²) or see 2x²+8x as (2x)(x)+(2x)(4), thus recognizing it as a polynomial whose terms are products of monomials and the polynomial can be factored as 2x(x+4).

C. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

1. Factor a quadratic expression to reveal the zeros of the function it defines.

2. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

3. Use the properties of exponents to transform expressions for exponential functions emphasizing integer exponents.

Example: The growth of bacteria can be modeled by either f(t)=3^(t+2) or g(t)=9(3^t) because the expression 3^(t+2) can be rewritten as (3^t)(3²)=9(3^t).

D. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

E. Identify zeros of quadratic functions and use the zeros to sketch a graph of the function defined by the polynomial.

F. Create equations and inequalities in one variable and use them to solve problems. (Include equations arising from linear, quadratic, and exponential functions.)

G. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

H. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

Example: Represent inequalities describing nutritional and cost constraints on combinations of different foods.

I. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

Example: Rearrange Ohms law V=IR to highlight resistance R.

J. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

K. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

L. Solve quadratic equations in one variable.

1. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x - p)2 =q that has the same solutions. Derive the quadratic formula from this form.

2. Solve quadratic equations by inspection (e.g., for x²=49), taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as "no real solution."

M. Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

N. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

O. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

P. Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x) =g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, piecewise linear (to include absolute value), and exponential functions.

Q. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

La. Admin. Code tit. 28, § CLXXI-2103

Promulgated by the Board of Elementary and Secondary Education, LR 421057 (7/1/2016).

AUTHORITY NOTE: Promulgated in accordance with R.S. 17.6, R.S. 17:24.4, and R.S. 17:154.